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    A Fictitious Time Integration Method for Multi-Dimensional Backward Heat Conduction Problems

    Chih-Wen Chang1

    CMC-Computers, Materials & Continua, Vol.19, No.3, pp. 285-314, 2010, DOI:10.3970/cmc.2010.019.285

    Abstract In this article, we propose a new numerical approach for solving these multi-dimensional nonlinear and nonhomogeneous backward heat conduction problems (BHCPs). A fictitious time t is employed to transform the dependent variable u(x, y, z, t) into a new one by (1+t)u(x, y, z, t)=: v(x, y, z, t, t), such that the original nonlinear and nonhomogeneous heat conduction equation is written as a new parabolic type partial differential equation in the space of (x, y, z, t, t). In addition, a fictitious viscous damping coefficient can be used to strengthen the stability of numerical integration of the discretized equations… More >

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